In populous metropolitan areas, the free-floating bicycle sharing system (FFBSS) acts as an innovative urban mobility-as-a-service (MaaS), which provides an ease-of-use feature and extra flexibility in contrast to the traditional shared bicycles with docks. In consideration of customer behaviors such as abandonment and retrial which occur in FFBSS, a redistribution strategy for shared bicycles among different user-density locations is presented, with an aim to diminish the total operational cost while enhancing the overall service level. To formulate the user and multi-type shared bicycle arrival patterns as non-homogeneous queues, our results provide a tractable analytical paradigm for time-varying balancing strategy for FFBSS. The bicycle variation at each virtual zone after each redistribution is determined via a non-stationary queueing model, where the service time, patience time and re-search delay are all subject to general distribution. Then the bicycle deployment strategy is evaluated with respect to average queueing length and abandonment rate during a normal workday based on a tailored nonhomogeneous probabilistic matching queue. To verify the efficacy and cost-effectiveness of the proposed bicycle redistribution strategy, multiple simulation runs are conducted with respect to various time of the day. It shows that the resulting optimal rebalancing strategy is batch-based, in synchrony with the time heterogeneity in the traffic demand. Furthermore, several managerial insights are provided to shed light on the rule-of-thumb in practical FFBSS redistribution coordination.